Permanent regimes for the Vlasov-Maxwell equations with specular boundary conditions

Kinetic Equations with Maxwell Boundary Condition

We prove global stability results of DiPerna-Lions renormalized solutions to the initial boundary value problem for kinetic equations. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which include the so-called Maxwell boundary condition, and we prove that it is realized (it is not relaxed!). The techniques are illustrated with the Fokker-Planck-Boltzmann equat...

Permanent Regimes for the 1D Vlasov-Poisson System with Boundary Conditions

Kinetic equations with Maxwell boundary conditions

We prove global stability results of DiPerna-Lions renormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a bounda...

Stability Analysis of Collisionless Plasmas with Specularly Reflecting Boundary

Abstract In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at the boundary for the particles and with the perfectly conducting boundary condition for the electromagnetic field. Here we initiate our investigation...

On the harmonic Boltzmannian waves in laser-plasma interaction

We study the permanent regimes of the reduced Vlasov–Maxwell system for laser-plasma interaction. A non-relativistic and two different relativistic models are investigated. We prove the existence of solutions where the distribution function is Boltzmannian and the electromagnetic variables are time-harmonic and circularly polarized.